We consider the ground state of the one-dimensional quantum Ising model with transverse field hx in one dimension depending on the site xZ in a finite volume Λm ≔ {−m, −m + 1, …, m + L}. We make suitable assumptions on the regions where the field is small and prove that if the field is sufficiently large on the complementary set, then the entanglement of the interval Λ00,..,L relative to its complement Λm0 is bounded uniformly in m and L. The result applies in particular to periodic transverse fields. The bound is established by means of a suitable cluster expansion.

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